Domain epitaxy for thin film growth

ABSTRACT

A method of forming an epitaxial film on a substrate includes growing an initial layer of a film on a substrate at a temperature T growth , said initial layer having a thickness h and annealing the initial layer of the film at a temperature T anneal , thereby relaxing the initial layer, wherein said thickness h of the initial layer of the film is greater than a critical thickness h c . The method further includes growing additional layers of the epitaxial film on the initial layer subsequent to annealing. In some embodiments, the method further includes growing a layer of the film that includes at least one amorphous island.

RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.11/038,008, filed Jan. 18, 2005, which is a continuation of U.S.application Ser. No. 10/608,780 (now allowed), filed on Jun. 27, 2003,which claims the benefit of U.S. Provisional Application No. 60/393,008,filed on Jun. 28, 2002 and U.S. Provisional Application No. 60/479,206,filed on Jun. 17, 2003. The entire teachings of the above applicationsare incorporated herein by reference.

INCORPORATION BY REFERENCE

The entire teachings of the following are incorporated herein byreference:

-   U.S. application Ser. No. 11/038,008, filed Jan. 18, 2005;-   U.S. application Ser. No. 10/608,780 filed on Jun. 27, 2003;-   U.S. application Ser. No. 10/463,219 filed on Jun. 17, 2003;-   U.S. Provisional Application No. 60/479,206, filed on Jun. 17, 2003;-   U.S. Provisional Application No. 60/393,008, filed on Jun. 28, 2002;-   U.S. Provisional Application No. 60/389,750, filed on Jun. 17, 2002;-   U.S. patent application Ser. No. 10/187,466, filed on Jun. 28, 2002-   U.S. patent application Ser. No. 10/187,465, filed on Jun. 28, 2002-   U.S. patent application Ser. No. 10/187,468, filed on Jun. 28, 2002;    and-   U.S. Pat. No. 5,406,123.

GOVERNMENT SUPPORT

The invention was supported, in whole or in part, by a grant from theNational Science Foundation and by the U.S. Department of Energy underthe Contract No. DE-AC05-00OR22725 and Contract No. W-31-109-ENG-38. TheGovernment has certain rights in the invention.

BACKGROUND OF THE INVENTION

Epitaxial growth of thin films and control of defects in thin filmheterostructures are key considerations for the next-generationmicroelectronic, optical and magnetic devices (H. J. Queisser and E. E.Haller, Science (1998) 281: 945, S. Nakamura, Science (1998) 281: 956,S. Mahajan, Acta Mater. (2000) 48: 137). As device feature sizes aregetting smaller, a single dislocation is liable to control the deviceperformance. In the well-established lattice-matching-epitaxy, wherelattice misfit is small (i.e. less than 7-8%) the film growspseudomorphically up to a certain thickness (critical thickness) beforeit becomes energetically favorable for the film to contain dislocations(J. W. Mathews and A. E. Blakeslee, J. Crystal Growth (1974) 27: 188, J.W. Mathews in “Epitaxial Growth”, Part B, Materials Science Series(1975) 560, Academic Press, New York). In this case, the dislocationsare generated at the surface and then they glide to the interface. TheBurgers vectors and planes of the dislocations are dictated by the slipvectors and glide planes of the crystal structure of the film (J.Narayan and S. Sharan, Mat. Sci. Engineering B (1991) 10: 261). On theother hand, if the dislocations are generated at the edge of islandsduring three-dimensional growth, the geometrical constraints determinethe Burgers vectors of the dislocations, which lie in the film-substrateinterface. For example, during three-dimensional growth of germanium onsilicon, it was found that 90⁰ dislocations with a/2<110> Burgersvectors were created at the edge of germanium islands lying in the (001)film-substrate interface (F. K. LeGoues et al. Phys Rev. Lett. (1994)73: 300). It is believed that the lattice matching epitaxy during thinfilm growth is possible as long as the lattice misfit between the filmand the substrate is less than 7-8%. Smaller lattice misfit leads tosmaller interfacial energy and coherent epitaxy is formed. Above thismisfit the film generally will grow in a textured or largelypolycrystalline manner. Such films contain plane boundaries. Plainboundaries consist of dislocation, which impede charge carrier movementand thus deleteriously affect the performance of semiconductor devices.

Accordingly, there is a need for electronic and semiconductor deviceswhere a single crystal thin film layer of arbitrary crystal structure isepitaxially grown on top of a pre-selected substrate and where a latticemisfit between the epitaxial layer and the substrate is arbitrarilylarge.

SUMMARY OF THE INVENTION

In general, the instant invention relates to domain-matched epitaxialgrowth of a film on top of a substrate, whereby the integral multiplesof lattice planes match across the film-substrate interface.

The method of the invention includes forming an epitaxial film on asubstrate by growing an initial layer of a film on a substrate at atemperature T_(growth), said initial layer having a thickness h. Theinitial layer of the film is then annealed at a temperature T_(anneal)thereby relaxing the initial layer.

The advantages of the present invention include, for example, theability to design and grow essentially strain-free epitaxial films on asubstrate having arbitrarily large lattice misfit. Additional strainbeyond perfect domain matching is relieved by a systematic (periodic)variation in domain size resulting in relieving most of strain within acouple of monolayers of the epitaxial material, so that the rest of thefilm can be grown free from lattice strains and the attending defects.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plot of strain (lattice misfit) versus film-substrate planarspacing ratio. The LME region is above about 12/13 ratio or below about7.7% strain. The plot can be used to predict the planar spacing ratioand domain periodicity of an epitaxial layer grown according to themethod of the present invention.

FIG. 2 is a high-resolution microphotograph of a cross-section in <110>direction from the TiN/Si(100) system grown according to the method ofthe presemt invention. The microphotograph shows domain matching of TiNwith silicon. Here the frequency factor (α=0.5) for 4/3 and 4/5 domains.The a/2<110> misfit dislocations lie in {111} planes in both TiN andsilicon.

FIG. 3(a) is a microphotograph depicting domain epitaxy in AlN/Si(111)system, grown according to the method of the invention. Themicrophotograph of a high-resolution cross-section of a (01-10)AlNepitaxial layer and a (11-20)Si substrate is showing the matching ofAlN(2{overscore (11)}0) and Si(220)planes with α=0.25 for 4/5 and 5/6domains, while corresponding (inset) diffraction pattern shows thealignment AlN and Si planes.

FIG. 3(b) is a schematic of arrangement of atoms in the basal plane ofAlN and Si(111) system as grown by the method of the present invention.

FIG. 4(a) is a high resolution TEM cross-section with (01-10) foil planeof sapphire and (2-1-10) plane of ZnO showing domain epitaxy inZnO/αAl₂O₃(sapphire) system, grown according to the method of thepresent invention.

FIG. 4(b) is a Fourier-filtered image of a matching of (−2110) ZnO and(30{overscore (3)}0) sapphire planes of the system of FIG. 4(a) with thefrequency factor (α=0.5) for 5/6 and 6/7 domains.

FIG. 4(c) is a photograph of an electron diffraction patterncorresponding to FIG. 4(a), showing the alignment of planes in ZnO andsapphire.

FIG. 4(d) is a schematic of arrangement of atoms in the basal plane ofZnO and sapphire of the system of FIG. 4(a).

FIG. 5(a) and (b) show X-ray surface diffraction measurements along the(H, 0, −H, 0.3) direction showing the growth according to the method ofthe present invention of ZnO films on sapphire with sapphire in-planelattice parameter approaching H=0.845 corresponding to a fully relaxedposition after a few monolayers.

FIG. 6(a) and (b) are cross-section TEM micrographs from ZnO/Sapphirespecimens grown according to the method of the present invention undertwo different diffraction conditions (g vectors) showing low density ofthreading dislocations, stacking faults and domain boundaries. Most ofthe dislocations are confined to the interface.

DETAILED DESCRIPTION OF THE INVENTION

The foregoing and other objects, features and advantages of theinvention will be apparent from the following more particulardescription of preferred embodiments of the invention, as illustrated inthe accompanying drawings in which like reference characters refer tothe same parts throughout the different views. The drawings are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the invention.

It has now been discovered that a new technique allows epitaxial growthof films with any lattice misfit on a given substrates with atomicallyclean surfaces.

As used herein the term “lattice misfit,” also referred to as “unrelaxedmisfit strain,” is defined as ε_(c)=a_(f)/a_(s)−1, where a_(f) and a_(s)are lattice constants of the film and the substrate, respectively.

As used herein, the term “epitaxy” refers to a process in which a thinlayer, referred to as a “film,” of a single crystal material isdeposited on a single crystal substrate in such a manner that thecrystallographic structure of the substrate is reproduced in the growingfilm. The term “heteroepitaxy” refers to an epitaxial growth whereinchemical composition of an “epi” material, i.e. a film, is differentfrom the chemical composition of the substrate. Epitaxy can be achievedby any of the methods known in the art. Such methods include pulsedlaser deposition (PLD), chemical vapor deposition (CVD), metal-organicvapor deposition (MOCVD), and molecular beam epitaxy (MBE).

In PLD, high-power pulsed laser beams are used to ablate the target in avacuum (less than about 10⁻⁶ torr) or a controlled atmosphere. Thisproduces a film of the same composition as the target.

In CVD, epitaxial growth is implemented by means of chemical reaction ofa gas-phase epi material with an exposed solid substrate. The MOCVD is asimilar procedure commonly used when the epi material is a III-Vsemiconductor. MBE, is a method of epitaxial growth wherein physicaldeposition of the epi material is carried out in ultra-high vacuum (atabout 10-8 torr) and at the substrate temperatures not exceeding about800° C. In MBE, an stream (a beam) of the molecules of the epi materialis directed at a chemically clean substrate surface.

As used herein, the term “domain” refers to a portion of an interfacebetween a substrate and an epitaxially grown layer comprising a wholenumber “n” of lattice planes on the substrate side of the interface,said planes having a separation distance “d_(s)” and a whole number “m”of lattice planes on the epitaxial layer side of the interface, saidplanes having a separation distance “d_(f)” and wherein the distancesbetween the maximally separated planes within the portion of theinterface on either side is about equal. As used herein, the term“domain-matching” refers to a step of forming at least one domain asdefined above in a process of growing an epitaxial layer on a substrate.

As used herein, the term “critical thickness” refers to a thickness of afilm, such that it becomes energetically favorable for the film tocontain dislocations if the thickness of the film is above the criticalthickness.

As used herein, the term “relaxation” refers to orienting the components(asymmetric units such as atoms or molecules) of a material of a film sothat said orientation is energetically most favorable. Relaxation ismeasured by a degree of difference between the experimentally measuredlattice constant of a material and the equilibrium value of the latticeconstant. As used herein, the term “complete relaxation” refers to astate of a material wherein the lattice constant of the material isequal to the equilibrium lattice constant of this material.

According to the method of the present invention, the integral multiplesof lattice planes match across the film-substrate interface, and thesize of the domain equals the integral multiples of planar spacing.Furthermore, the size of the domain can be varied periodically toaccommodate the lattice misfit that is not accommodated by perfectmatching.

Without being limited to any particular theory, it is believed that thetheoretical basis of the invention is as follows.

Fundamental Considerations in Domain-Matched Epitaxy

In domain matching epitaxy (DME), matching of lattice planes isconsidered, which could be different in different directions of thefilm-substrate interface. In the DME framework, the crystal structure ofthe film can have either the same or different orientation relationshipwith the substrate, depending on the nature of the misfit. The misfit isaccommodated by matching of integral multiples of lattice planes, andthere is one extra half-plane (dislocation) corresponding to eachdomain. The misfit can range from being very small to very large. In acase of relatively small misfit, the DME reduces to the conventionallattice matching epitaxy (LME), where matching of the same planes orlattice constants is considered with a misfit typically less that about7-8%. If the misfit falls in between the perfect matching ratios ofplanes, then the size of the domain can vary in a systematic (periodic)way to accommodate the additional misfit. In LME, the unrelaxed misfitstrain ε_(c) is less than 7 to 8% and is relaxed by the introduction ofdislocations beyond the critical thickness during thin film growth. InDME, the matching of lattice planes of the film (separated by distanced_(f)) with the those of the substrate (separated by distance d_(s))with similar crystal symmetry is considered. In DME, the film and thesubstrate planes could be quite different as long as they maintain thecrystal symmetry. The LME, on the other hand, involves the matching ofthe same planes between the film and the substrate. In DME, the initialmisfit strain (ε=d_(f)/d_(s)−1) could be very large, but can be relaxedby matching of m planes of the film with n of the substrate. Thismatching of integral multiples of lattice planes leaves a residualstrain of ε_(r) given byε_(r)=(md _(f) /nd _(s)−1)  (1),where m and n are integers. In the case of a perfect matchingmd_(f)=nd_(s),and the residual strain ε_(r) is zero. If ε_(r) is finite, then twodomains may alternate with a certain frequency to provide for a perfectmatching according to,(m+α)d _(f)=(n+α)d _(s)  (2),where α is a frequency factor. For example, if α=0.5, then m/n and(m+1)/(n+1) domains alternate with equal frequency.

Assuming d_(f)>d_(s), we have n>m. Therefore,n−m=1 or f(m)  (3).The difference between n and m could be 1 or some function of m,corresponding to the lowest energy of the system.

From equations (1) through (3), thye following equation can be derived,(m+α)ε=1 or f(m)  (4).Equation (4) governs the domain epitaxy. FIG. 1 shows a general plot ofmisfit percent strain as a function of ratio of film/substrate latticeconstants of major planes matching across the interface. In FIG. 1,n−m=1 for ε=0-50% and n−m=f(m) for ε=50 to 100%.

Table I provides a summary of different systems, which have been grownwith various misfit strains. Table I also includes the systems, whichfall in between the two domains, where two domains alternate withperiodicity needed for a essentially complete relaxation. TABLE I DomainEpitaxy for Thin Film Growth Planar spacing Strain m/n ratioExperimental Examples ∈ %  1/10 0.1 90.0% 1/9 0.11 88.8% 1/8 0.125 87.5%1/7 0.143 85.7% 1/6 0.166 83.3% 1/5 0.20 80.0% 1/4 0.25 75.0% 1/3 0.3366.7% 1/2 and 1/3 0.33-0.50 Mo, Nb, Ta, W/Si; Ni₃Al/Si(100) 50.0% 1/20.50 Fe/Si, Cr/Si, NiAl//Si(100) 2/3 0.666 Cu/Si(100) 33.33%  1/{squareroot over (2)} 0.707 SrTiO3/Ge(100) 29.28%  3/4 0.750 TiN/Si(100)25.00%  4/5 0.80 AlN/Si(111) 20.00%  5/6 0.83 α-Al₂O₃/ZnO(0001), 16.67% 6/7 0.857 α-Al₂O₃/ZnO(0001), Cu/TiN(100) 14.29%  7/8 0.8750α-Al₂O₃/GaN(0001) 12.50%  8/9 0.888 α-Al₂O₃/AlN(0001) 11.11%   9/10 0.90Y₁₂₃/MgO(001) 10.0% 11/12 0.9166 Y₁₂₃/MgO(001) 8.33% 12/13 0.9230STO/MgO(001) 7.69% 13/14 0.3286 7.14% 14/15 0.9333 6.67% 16/17 0.94125.88% 17/18 0.9444 5.55% 18/19 0.9474 5.26% 19/20 0.9500 5.00% 20/210.9524 4.76% 22/23 0.9556 4.35% 24/25 0.96 Ge/Si(100)  4.0% 31/32 0.96873.13% 49/50 0.98 Ge—Si/Si(100)  2.0%

It should be noted that a 45° rotation in some cubic systems and a 30°rotation in certain hexagonal systems are part of the domain-matchingconcept involving the matching of major planes between the film and thesubstrate. The plot in FIG. 1 provides a unified view oflattice-matching and domain-matching epitaxy with misfit strain rangingfrom 2-90% (50% corresponding to 1/2 matching). If the domain matchingis not perfect, epitaxy occurs by accommodating the additional misfit bychanging the domain size, controlled by the parameter α. In thisframework, it is important to realize that the nature of dislocationsremains the same, only their periodicity changes.

Lattice Relaxation and Defect Reduction

The rapid relaxation process of DME is consistent with the fact that thecritical thickness under relatively large misfits is less than 1monolayer. As a result, dislocations can nucleate during initial stagesof growth and confine most of the defects near the interface, leavingfewer defects near an active region of a device.

Since the critical thickness at which it becomes energetically feasiblefor the film to contain dislocations is less than one monolayer, thedislocations nucleate at free-surface steps within 1 monolayer andlocate at the interface where there is an energy minimum. An importantconsideration here is a large number density of surface steps within themonolayer, which can provide easy nucleation sites for dislocations. Ifthe initial growth is two-dimensional, the dislocations can propagatethroughout the entire length of the film and confine themselves near theinterface without creating threading dislocations. However, if theinitial growth is a mixture of two-dimensional (2D) andthree-dimensional (3D) growth, then dislocation segments may notpropagate throughout the entire length and threading segments may form.Depending upon the nature of growth characteristics and the numberdensity of surface steps, this consequence of DME can be used to reducethe number density of threading dislocations and confine most of themisfit dislocations near the interface.

However, if the critical thickness is relatively large in a low-misfitsystem, then the dislocations nucleate at the free-surface steps andthen glide to the interface. The process creates a half-loopconfiguration with two threading segments and a straight segment alongthe interface. Since there is a nucleation barrier for the dislocation,misfit is not fully relaxed. In addition, threading segments do notexpand to the edges due to the presence of other dislocations andobstacles, and as a result, a high density of these dislocations isretained within the film. Since these dislocations are purely glide orslip dislocations, their planes and Burgers vectors are controlled bythe slip systems of the film. The relaxation process in low-misfitsystems is gradual due to this nucleation barrier, leading to a largenumber of threading dislocations.

PREFERRED EMBODIMENTS OF THE INVENTION

Using the method of the present invention, films having larger misfitscan be grown with fewer defects in the active region than generallyoccur by employment of conventional techniques.

In one embodiment, the present invention is a method of forming anepitaxial film on a substrate. The surface of the substrate preferablyis atomically clean. Materials of a film and a substrate preferably haveinteratomic potentials that are not substantially different. Mostpreferably, the interatomic potentials do not differ by more than afactor of two. Materials of the film and of the substrate are furtherselected so that the symmetry of the crystal structures of two materialsis similar. Examples of crystal structures with similar symmetries aretwo structures that have at least one symmetry element in common.

The method comprises the steps of growing an initial layer of a film ona substrate at a temperature T_(growth), said initial layer having athickness h, and annealing the initial layer of the film at atemperature T_(anneal), thereby relaxing the initial layer. Preferably,the method further includes growing additional layers of the film. Mostpreferably, said thickness h of the initial layer of the film is greaterthan a critical thickness h_(c).

As used herein, “T_(growth)” is a temperature sufficient to form aninitial layer. As used herein, the term “annealing” refers to holdingthe initial layer without further deposition of film material at atemperature T_(anneal) for a non-zero period of time. In one embodiment,the period of time during which the formed initial layer is annealedcauses substantially complete relaxation of the crystal structure of thematerial of the initial layer. Preferably, the period of time duringwhich the formed initial layer is annealed causes essentially completerelaxation of the crystal structure of the material of the initiallayer. As used herein, “essentially complete relaxation” means thatthere is no detectable difference between an experimentally measuredlattice constant and an equilibrium lattice constant.

As used herein, “T_(anneal)” is a temperature at which the formedinitial layer is held without further depositing film material for aperiod of time sufficient to permit relaxation. In one embodiment, theperiod of time is sufficient to permit substantially completerelaxation. In another embodiment, the period of time is sufficient topermit essentially complete relaxation.

As used herein, “h” is a height of an initial layer formed duringdeposition of film material prior to annealing. The value of h can bemeasured either in Angstroms or in monolayers of atoms of the film.

Preferably, h is greater than h_(c). Generally, h is between about 1 andabout 10 monolayers. Preferably, h is between about 1 and about 5monolayers.

Temperature T_(growth) can be about equal to T_(anneal) or T_(growth)can be less than T_(anneal). The time required for annealing isdependent on temperature T_(anneal): the higher the annealingtemperature, the less time is required for annealing. Preferably,T_(growth) is between about 500° C. and 1000° C. More preferably,T_(growth) is between about 500° C. and about 750° C. T_(anneal) ispreferably between about 500° C. and about 1000° C. More preferably,T_(anneal) is between about 700° C. and 900° C.

Growth and annealing can independently be performed for a period of timefrom about 5 seconds to about 5 minutes. Preferably, growth andannealing can independently be performed for a period of time from about1 minute to about 2 minutes.

The growth of the initial layer can be three-dimensional ortwo-dimensional. Two-dimensional growth is preferred.

In another embodiment, the method of the present invention furtherincludes the step of growing a layer of the film that includes at leastone area of amorphous growth. Areas, or “islands,” of amorphous growthcan generally be created by using either impurities (dopants) that existin film material or by introduction of new or additional impurities.Many dislocations that would otherwise propagate beyond the initiallayer of film subsequent to relaxation terminate at the islands. As usedherein, “introduction of additional impurity” refers to increasingconcentration of a dopant that is already present in the material of thefilm.

Preferably, suitable impurities exist in the material of the layer and,upon introduction of additional impurity, either alone or in combinationwith the material deposited as the film can form amorphous phase.Examples of suitable impurities are silicon and germanium. Silicone orgermanium oxides and nitrides can form an amorphous phase. One ofordinary skill in the art can readily identify other suitableimpurities. As a non-limiting example, a layer of a GaN film includingat least one area of amorphous growth that includes silicon nitride orsilicon oxide can be produced. After the initial layer is deposited andrelaxed, the growth continues using MOCVD or pulsed laser depositiontechniques, described below, until the film is about 1000 Å thick. Then,silane and ammonia, if MOCVD is employed, or silicon and nitrogen gas,if the pulsed laser deposition technique is employed, are used forSiN_(x) formation, where x is between about 0.5 and about 1.33. Thetemperature for this process is from about 800° C. to about 1000° C.Alternatively, to form SiO_(y), where y is between about 0.5 and about2, silane and nitrous oxide (N₂O) at a temperature of from about 400° C.to about 500° C. are used.

The methods of the present invention generally can incorporate any ofthe epitaxy techniques known in the art. In a preferred embodiment, anapparatus as described in U.S. Pat. No. 5,406,123 is used. While,according to the present invention, overlayers, such as TiN, AlN onSi(100) and ZnO on α-Al₂O₃(0001), are preferably formed using pulsedlaser deposition processes as described in J. Narayan et al., Appl.Phys. Lett. (1992) 61:1290, the entire teachings of which are hereinincorporated by reference, it is to be understood that layers may beformed using various known processes including, but not limited to,molecular beam epitaxy (MBE), hydride vapor phase epitaxy (HVPE),magnetron sputtering techniques, and chemical vapor deposition (CVD).

The method of the present invention can be employed to producecomponents of various devices such as light-emitting diodes, laserdiodes, UV detectors, and/or broad spectrum (e.g. white) light sourcesused, for example, in light bulbs. Microelectronic devices manufacturedaccording to embodiments of the present invention can be transistorssuch as CMOS transistors, field-effect transistors, and/or bipolartransistors, diodes, field emitters, and/or power devices as well asother integrated circuit devices. Optoelectronic devices manufacturedaccording to the method of the present invention can provide junctionsbetween a substrate and a overlayer to provide LEDs, laser diodes, UVdetectors, broad band light sources, and/or other optoelectronicdevices. Junctions can be provided by doping and/or other techniques aswill be understood by those skilled in the art.

Exemplification

EXAMPLE 1 TiN Film on Si(100) Substrate Accommodates a 22% Misfit

Epitaxial growth of TiN on silicon substrate represents a majormilestone for next-generation semiconductor devices for direct ohmiccontacts as well as for discussion barriers in copper metallization.However, with a misfit of over 22% for cube-on-cube TiN (a=0.424 nm)epitaxy over silicon (a=0.543 nm), it is beyond the critical strain(approximately 7-8%) of conventional lattice matching. However,epitaxial growth of TiN on silicon substrate was demonstrated by theconcept of domain matching epitaxy. The films were grown using astandard pulsed laser deposition method known in the art. Briefly, theinitial layer of TiN of thickness h about 1-2 monolayers was depositedat T_(growth) of between about 600° C. and 650° C. and then annealed atT_(anneal) of about 750° C. for about 1 to about 2 minutes. Afterannealing, the growth was resumed at T_(growth).

FIG. 2 shows a detailed high-resolution cross-section TEM micrograph,where the 3/4 and 4/5 domains alternate. The micrograph was taken in the<110> zone axis of Si and TiN, it is interesting to note the matching of{111} extra half planes in silicon as well as TiN. From FIG. 1, thelattice misfit of 22% lies in the middle 3/4 and 4/5 matching, whichexplains the alternating of domains. In fact with α=0.5 (see equation2), 3.5a_(Si)=19.01 matches quite well with 4.5×a_(TiN)=19.08, whichalso represents the size of domain for the system with virtually noresidual misfit.

The nature of dislocations can be established directly from thehigh-resolution TEM micrographs. The Burgers vector of the dislocationsis determined to be a/2<110> lying in {111} planes. The two sets ofa/2<110> dislocations combine at the interface to produce a/2<110>dislocations lying in the {001} interface. This dislocation reaction canbe described as: a/2[101](11-1)+a/2[01-1](111)→a/2[110](001). In somecases, the dislocations do not combine and create an extended corestructure associated with the pair of dislocations. The formation ofa/2<110> dislocations in {111} plane in TiN with a sodium chloridestructure represents a significant finding. The TiN having a sodiumchloride structure has {11 0} slip planes with a/2<110> Burgers vectors.Only under certain extreme nonequilibrium conditions such as high field,a/2<110> lying in {001} planes have been observed (18). However, this isfirst for a/2<110> dislocation in {111} planes of sodium chloridestructure. These new dislocations or slip systems may impact mechanicaland physical properties of TiN films or materials of sodium chloridestructure, in general, in a significant way. According to von Misescriterion, five independent slip systems are needed for a crystal toundergo a plastic deformation by slip. In TiN having a sodium chloridestructure, there are only two independent a/2<110>{110} slip systemsavailable, which restricts a general deformation, resulting in twinningand fracture. However, with a/2<110>{111} slip systems, there are 384ways of choosing five independent slip systems, which can lead to ageneral deformation of TiN (J. P. Hirth and J. Lothe, Theory ofDislocations, P. (1998) John Wiley, New York).

EXAMPLE 2 Variations in Domain Size Accommodate a 20% Strain inIII-nitride Epitaxy on Si(111) System

Epitaxial growth of III-nitrides having a wurtzite structure on silicon(111) substrates are needed as a template to grow GaInN and AlGaInNalloys as well as to integrate III-nitride based optoelectronic deviceswith microelectronic devices. Additionally, AlN has high thermalconductivity (320 w/MK), high thermal stability (up to 2200° C.), highresistivity (10¹³ Ω-cm), high dielectric strength (14 kV/cm), and highchemical inertness. The hardness and thermal expansion coefficient(2.56×10⁻⁶/K are comparable to that of silicon. The above propertiesmake AlN an ideal candidate for application in microelectronic tooptoelectronics including high-temperature devices and electronicspackaging.

Epitaxial growth of AlN (0001) with hexagonal wurtzite structure (a=3.11A, c=4.982A) on silicon (111) substrate occurs via matching of foursilicon (220) planes with five (2{overscore (11)}0) planes of AlN. Thespacing of (2{overscore (11)}0)AlN planes (a/2=1.556A) result is closeto 19% strain with (220) planes of silicon. Using this strain, we foundby using the plot in FIG. 1 that, 5 AlN (2{overscore (11)}0)/4 (220)matching results with less than 1% residual strain.

Using the standard pulsed laser deposition technique known in the art,we have grown an epitaxial film of AlN (0001) having a hexagonalwurtzite structure on silicon (111) substrate. Briefly, the initiallayer of AlN of thickness h about 1-2 monolayers was deposited atT_(growth) of about 650° C. and then annealed at T_(anneal) of about800° C. for about 1 to about 2 minutes. After annealing, the growth wasresumed at T_(growth).

FIG. 3(a) shows a cross-section TEM micrograph where the alignment of(2{overscore (11)}0) planes of AlN with (220) planes of silicon isclearly delineated. The (111) planes of silicon substrate are shownschematically in FIG. 3(b) on which basal planes of AlN {0001} grow witha-axis of AlN [2{overscore (11)}0] aligned with [220] direction ofsilicon. In this field of view, five planes of AlN clearly match withfour planes of silicon with one exception where six planes of AlN matchwith 5 planes of silicon. This is predicted from our master diagram inFIG. 1 for a 19% strain. The perfect matching is predicted from equation(3) for α=0.25. Thus, the deviations from the ideal 5/4 matching(corresponding to 20% strain) are accommodated by variation in domainsize, rather than an additional set of secondary dislocations to relievethe difference in the strain from the ideal 5/4 matching.

EXAMPLE 3 Domain Epitaxy of Wurtzite Hexagonal ZnO on α-Al₂O₃(0001)

There is a growing interest in growing high quality thin films of ZnOand its alloys for light emitting diodes (LEDs) and laser diodes (LEDs)applications. The bandgap of ZnO can be tuned by alloying with MgO (8.0eV, upshift) or with CdO (1.9 eV, downshift). The ZnO can be also usedas a template for III-nitride growth separately as well as on sapphiresubstrates. Therefore, the growth of high quality ZnO (having wurtzitehexagonal structure, a=3.252 A, c=5.213 A) on a practical substrate suchas sapphire (a=4.758 A, c=12.991 A) presents a major challenge. Thegrowth of systems with such a relatively large misfit is possible onlywith domain matching epitaxy, where the misfit can be accommodated thematching of planes.

Using the standard pulsed laser deposition technique known in the art,we have grown an epitaxial film of ZnO having a hexagonal wurtzitestructure on silicon (111) substrate. Briefly, the initial layer of ZnOof thickness h about 1-2 monolayers was deposited at T_(growth) of about650° C. and then annealed at T_(anneal) of about 700° C. for about 1 toabout 2 minutes. After annealing, the growth was resumed at T_(growth).

FIG. 4(a) shows a high-resolution cross-section TEM micrograph where theZnO film plane is (2-1-10) and the sapphire substrate is (01-10). Theepitaxial growth of ZnO film with atomically sharp interface is clearlydemonstrated. The Fourier-filtered image in FIG. 4(b) clearly delineatesthe matching of 5 or 6 (−2110) planes of ZnO with (30{overscore (3)}0) 6or 7 planes of sapphire. The corresponding diffraction pattern, whichconfirms this alignment of planes, is shown in FIG. 4(c). The c-plane ofZnO rotates by 30° in the basal c-plane of sapphire as shown in FIG.4(d), which leads to alignment of ½ (30{overscore (3)}0) planes ofsapphire with (2{overscore (11)}0) planes or ‘a’ planes of the ZnO film.Thus, we are looking at domain matching of sapphire planes (havinga_(sap)/√3 spacing) with ‘a’ planes of ZnO. By alternating the domains,there is almost a perfect matching as 5.5×a_(ZnO) (3.2536)≈6.5 α-Al₂O₃(2.7512), as predicted for α=0.5 from equation (3). These numbersinclude planar spacings at the growth temperature, taking into accountthe respective coefficients of thermal expansion. From the planarspacing, we calculate the strain of 15.44%, which falls in between 5/6and 6/7 matching in the master plot of FIG. 1. This is in completeagreement with experimental observation of FIG. 4(a) and FIG. 4(b).

EXAMPLE 4 In situ X-Ray Diffraction Measurements Show CompleteRelaxation After Deposition of Two Monolayers

The critical thickness for this system is less than one monolayer. Twomonolayers of ZnO were grown at 585 to 600° C. Annealing was performedeither at 700° C. for about 10 minutes or 800° C. for about 1 minute.After annealing, the growth was resumed at 585 to 600° C.

The details of lattice relaxation process during initial stages of ZnOgrowth on sapphire (α-Al₂O₃), (0001)) substrates have been studied byin-situ x-ray diffraction study using the UNI-CAT undulator beam line atthe Advanced Photon Source. In these experiments, the laser-ablation,filmgrowth chamber is mounted on a so-called 2+2 x-ray diffractometerwhere surface scattering measurements in specular and off-speculardirections were made to investigate the details of initial stages ofthin film growth. Time-slice x-ray crystal truncation rod (CTR)measurements made after each excimer laser ablation pulse revealed thesurface structure transients associated with ZnO clustering andcrystallization to last about 2 s following the abrupt ˜5 μs duration oflaser deposition.

Specular CTR anti-Bragg measurements at the sapphire (0 0 5/2) positionshowed only one well-defined growth oscillation, indicatingthree-dimensional (3D) growth rather than layer by laser growth.Off-specular CTR measurements along the (H, 0, −H, 0.3) direction showedthermally activated relaxation of the 15.44% lattice mismatch betweenZnO and Al₂O₃ along with a 30° in-plane rotation around the c axis. Asshown in FIG. 5, a broad, nearly relaxed ZnO in-plane diffraction peakappears after the deposition of 3 monolayers at 400° C. (˜25pulses/monolayer), while a sharper and more fully relaxed ZnO peakappears after only 2 monolayers at 585° C. The peak after 150 pulses at585° C. occurs at H=0.845 corresponding to the fully relaxed ZnO film.Subsequent measurements (not plotted here) showed that incommensurationoccurs within the first layer of the deposition, and the nature of thestrain is compressive as expected for matching of a planes of ZnO(spacing 3.2536 Å) with underlying sapphire planes (2.7512 Å). Theseresults clearly established a rapid relaxation of ZnO films on sapphire.The relaxation process was found to be thermally activated because theZnO thickness corresponding to complete relaxation decreased as thedeposition temperature increased. The relaxation process requires thecreation of dislocations, which involves nucleation and propagation ofdislocations. Both of these steps are thermally activated. Thenucleation barrier can be partially overcome by the surface steps, andthe propagation is very small in DME due to the proximity of theinterface.

EXAMPLE 5 Dislocations are Confined to the Inteface in ZnO/SapphireSpecimens

FIG. 6(a) and FIG. 6(b) show TEM cross-section of ZnO/Saphhirespecimens, grown as described in Example 4, under two differentdiffraction conditions to image dislocations.

From these micrographs, the density of threading dislocations withBurgers vector b=1/3[11-20] was estimated to be 10⁷ cm⁻², which is threeorders of magnitude lower than normally observed for the misfit of thismagnitude (15.44%). The density of stacking faults (planar defects) wasestimated to be 10⁵ cm⁻¹. It is interesting to note that most of thedislocations and other defects (stacking faults and domain boundaries)are confined to the ZnO/Sapphire interface as expected from domainepitaxy.

Equivalents

While this invention has been particularly shown and described withreferences to preferred embodiments thereof, it will be understood bythose skilled in the art that various changes in form and details may bemade therein without departing from the scope of the inventionencompassed by the appended claims.

1. A method of forming an epitaxial film on a substrate, comprising thesteps of: (a) growing an initial layer of a film on a substrate at atemperature T_(growth), said initial layer having a thickness h; (b)annealing the initial layer of the film at a temperature T_(anneal),thereby substantially completely relaxing the initial layer.
 2. Themethod of claim 1 further including growing additional layers of thefilm over the initial layer subsequent to annealing.
 3. The method ofclaim 1 wherein said thickness h of the initial layer of the film isgreater than a critical thickness h_(c).
 4. The method of claim 1wherein h between about 1 and about 5 monolayers.
 5. The method of claim1 wherein T_(growth) is about equal to T_(anneal).
 6. The method ofclaim 1 wherein T_(growth) is less than T_(anneal).
 7. The method ofclaim 1 wherein growth of the initial layer includes two-dimensionalgrowth.
 8. The method of claim 1 wherein the substrate includes Si(100)and the film includes TiN.
 9. The method of claim 1 wherein thesubstrate includes Si(111) and the film includes at least oneIII-nitride selected from the group consisting of AlN, GaInN, andAlGaInN.
 10. The method of claim 9 wherein the film includes AIN. 11.The method of claim 1 wherein the substrate includes Al₂O₃(0001) andwherein the film includes at least one member selected from the groupconsisting of ZnO, AlN, GaInN, and AlGaInN.
 12. The method of claim 11wherein the film includes ZnO.
 13. The method of claim 2 furtherincluding the step of growing a layer of the film that includes at leastone amorphous area.
 14. The method of claim 14 wherein at least oneamorphous area includes Si.
 15. The method of claim 14 wherein at leastone area of amorphous growth includes silicone nitride or siliconeoxide.